1. Field of the Invention
The present invention relates to cubic convolution interpolation, and more particularly, to a cubic convolution interpolating apparatus which can minimize information loss due to a change in the resolution of an image signal, and a method thereof.
2. Description of the Related Art
Cubic convolution interpolation, which is one of various techniques of scaling or resampling original image data, has been proposed for compensating for a disadvantage encountered by conventional interpolation techniques in which a sin c(x) function is used. The interpolation technique using sin c(x) has been proposed for attaining more ideal interpolation, when an interpolated continuous function {circumflex over (ƒ)}(x) for original image sample data ƒ(xk) is given by:
                                          f            ^                    ⁡                      (            x            )                          =                              ∑            k                    ⁢                                    c              k                        ⁢                          β              ⁡                              (                                  x                  -                                      x                    k                                                  )                                                                        (        1        )            which can then be rewritten, using a function of sin c(x), as:
                                          f            ^                    ⁡                      (            x            )                          =                              ∑            k                    ⁢                                    f              ⁡                              (                                  x                  k                                )                                      ⁢            sin            ⁢                                                  ⁢                          c              ⁡                              (                                  x                  -                                      x                    k                                                  )                                                                        (        2        )            wherein β(x) is a basis kernel function, ck is a coefficient concerning the image data of an arbitrary pixel, that is, ƒ(xk), x is an interpolation point of an arbitrary pixel, and xk denotes sample points of original image data.
However, since the sin c(x) function is defined in an infinite region, a vast quantity of data must be calculated, which makes actual implementation impossible. Thus, a function that can be used in lieu of the sin c(x) function has been developed by many researchers, and the cubic convolution interpolation is one of the representative interpolation techniques using the newly developed function.
The cubic convolution interpolation uses in lieu of sin c(x) a basis kernel function β(x) having an effective value in the region of (−2, 2), as represented by:
                              β          ⁡                      (            x            )                          =                  (                                                                                                                (                                              α                        +                        2                                            )                                        ⁢                                                                                          x                                                                    3                                                        -                                                            (                                              α                        +                        3                                            )                                        ⁢                                                                                          x                                                                    2                                                        +                  1                                                                              0                  ≤                                                          x                                                        ≤                  1                                                                                                                          α                    ⁢                                                                                          x                                                                    3                                                        -                                      5                    ⁢                    α                    ⁢                                                                                          x                                                                    2                                                        +                                      8                    ⁢                    α                    ⁢                                                                x                                                                              -                                      4                    ⁢                    α                                                                                                1                  ≤                                                          x                                                        ≤                  2                                                              )                                    (        3        )            
In other words, when s=x−xk and 1−s=xk+1−x in the relationship between an interpolation point x and an ambient sampling point s, 0≦s≦1 and xk≦x≦xk+1, by using the basis kernel function β(x) in lieu of sin c(x), a cubic convolution interpolated continuous function can be obtained, as represented by:
                                                                                          f                  ^                                ⁡                                  (                  x                  )                                            =                            ⁢                                                                    f                    ⁡                                          (                                              x                                                  k                          -                          1                                                                    )                                                        ⁢                                      {                                          α                      ⁡                                              (                                                                              s                            3                                                    -                                                      2                            ⁢                                                          s                              2                                                                                +                          s                                                )                                                              }                                                  +                                                                                                      ⁢                                                                    f                    ⁡                                          (                                              x                        k                                            )                                                        ⁢                                      {                                                                  α                        ⁡                                                  (                                                                                    s                              3                                                        -                                                          s                              2                                                                                )                                                                    +                                              (                                                                              2                            ⁢                                                          s                              3                                                                                -                                                      3                            ⁢                                                          s                              2                                                                                +                          1                                                )                                                              }                                                  +                                                                                                      ⁢                                                                    f                    ⁡                                          (                                              x                                                  k                          +                          1                                                                    )                                                        ⁢                                      {                                                                  α                        ⁡                                                  (                                                                                    -                                                              s                                3                                                                                      +                                                          2                              ⁢                                                              s                                2                                                                                      -                            s                                                    )                                                                    +                                              (                                                                                                            -                              2                                                        ⁢                                                          s                              3                                                                                +                                                      3                            ⁢                                                          s                              2                                                                                                      )                                                              }                                                  +                                                                                                      ⁢                                                f                  ⁡                                      (                                          x                                              k                        +                        2                                                              )                                                  ⁢                                  {                                      α                    ⁡                                          (                                                                        -                                                      s                            3                                                                          +                                                  s                          2                                                                    )                                                        }                                                                                                                                          wherein                  ⁢                                    ⁢                                      {                                          α                      ⁡                                              (                                                                              s                            3                                                    -                                                      2                            ⁢                                                          s                              2                                                                                +                          s                                                )                                                              }                                                  ,                                  {                                                            α                      ⁡                                              (                                                                              s                            3                                                    -                                                      s                            2                                                                          )                                                              +                                          (                                                                        2                          ⁢                                                      s                            3                                                                          -                                                  3                          ⁢                                                      s                            2                                                                          +                        1                                            )                                                        }                                ,                            ⁢                                                                                                      (        4        )            {α(−s3+2s2−s)+(−2s3+3s2)} and {α(−s3+s2)} are interpolation coefficients α is a parameter for varying the characteristic and shape of a basis kernel and determining the interpolation coefficient.
Rifman et al., (S. S. Rifman, Digital Rectification of ERTS Multispectral Imagery in Proc. Symp. Significant Results Obtained from ERTS-1(NASA SP-327), I, Sec. B, pp. 1131–1142, 1973) discloses an interpolation technique in which interpolation is performed by obtaining a cubic convolution interpolated continuous function such that α is set to −1 and the slopes of β(x) and sin c(x) coincide at a point where x=1. Keys et al. (R. G. Keys, Cubic Convolution Interpolation for Digital Image Processing IEEE transactions on Acoustic Speech Signal Processing, Vol. 29, pp.1153–1160, 1981) proposes an interpolation technique in which a is set to −½ and then a cubic convolution interpolated continuous function is obtained. However, according to these techniques, since α is a fixed value, a careful consideration cannot be taken into account for a variety of frequency characteristics of an image.
To overcome the drawback, Park et al. (S. K. Park and R. A. Schowengerdt, Image Reconstruction by Parameteric Cubic Convolution, Computer Visual Graphic Image Processing, Vol. 23, pp 258–272, 1983) proposes a cubic convolution interpolation technique in which α is used as a tuning parameter. According to this technique, optimized α is obtained by inferring the relationship between α and the frequency characteristic of original image data, and then the cubic convolution interpolation is implemented. However, according to this method, the optimized α is obtained by inferring the relationship between α and the overall frequency characteristic of one frame image to be processed. Thus, compared to the previous technique in which α is set to a fixed value, a consideration into the frequency characteristic of image data can be rather sufficiently taken. However, since α is inferred using the overall frequency characteristic of one frame image, in the case where the image has various spatial frequencies, the quantity of information loss associated with a change in the spatial frequency components becomes relatively increased, resulting in deterioration in the quality of scaled image data.